are all possible representations of 4 as a sum of powers of 2. The sequence \((b(n))_{n\in \mathbb {N}}\)  was already introduced by Euler. However, it seems that the first serious study of its properties was performed by Churchhouse [1]} in 1969. He computed the 2-adic valuation of \(b(n)\) . Further results, motivated by Churchhouse's computations, were obtained independently by Gupta [2]}, [3]}, [4]} and Rødseth [5]} (see also recent studies by Rødseth and Sellers [6]}).
